Critical Mass: How One Thing Leads to Another by Philip Ball 644pp, Heinemann, £25

"The great advantage of the mathematical sciences above the moral," wrote David Hume in 1748, "consists in this, that the ideas of the former are always clear and determinate."

For example, Hume went on, an oval is never mistaken for a circle, nor a hyperbola for an ellipsis. Yet for the moral sciences, which in the 18th century embraced the investigation of the mind and society as well as questions of right and wrong, there was no such precision. "Ambiguity," Hume said, "is gradually introduced into our reasonings." With that passage, from An Enquiry Concerning Human Understanding , the fat Scotsman waddled off to join the wildest wild-goose chase in the history of western thought, which is the attempt to capture for the various sciences of humanity the precision and prestige of mathematics. This yearning for universal mathematical laws to govern the behaviour of human beings has burdened the west with all sorts of harmless and less harmless nonsense, from phrenology to economics. It now finds a champion in Philip Ball in this long book.

Ball's argument is that this time, it's different, guv. In other words, mathematical and statistical physics has attained such a sophistication that its insights into the behaviour of particles of matter can be transferred to the mass behaviour of human beings, whether investing in the stock market or racing for the exits after a fire at a football ground.

In addition, and sotto voce, Ball tells us that society in mass has now become so mechanical that human beings really do resemble atoms of physical matter interacting with one another through forces of attraction and repulsion.

Will and personality are not abolished, we are told, in Ball's new "physics of society" but submerged into the averages rather as, in Dickens's Hard Times , the personality of each workman is absorbed into the industrial arithmetic of the mill. For a scientific book there is quite a lot of history. Ball writes clearly and is socko with graphs, but I found his arguments utterly unconvincing. Other readers may be more fortunate. In a series of short, bright chapters, Ball mines the specialist journals to provide the very latest applications of "social physics" to urban planning, the movement of pedestrians and motor traffic, stock price movements, trade, the rise and fall of corporations, diplomacy, political alliances, voting patterns, the composition of city neighbourhoods, criminology, matrimony, the transmission of culture and fashion, circles of acquaintance, the internet, sexual epidemiology, weapons of mass destruction. It soon becomes clear that this is not physics, but something that only looks and sounds and tastes and smells a bit like physics.

Whether the experiments concern pedestrians crossing the campus of Stuttgart University or Brazilians electing their state governments, Ball presents patterns and distributions which he says resemble those identified by physicists, such as the Ising model of how atoms magnetise or the sudden "phase transitions" that occur when water melts or freezes. The experiments in political or social organisation pro duce results that "parallel", "are equivalent of", "look exactly like", "are reminiscent of" patterns in experiments in natural science.

Ball is right, no doubt, that in a traffic jam on the bypass, human beings are not at their richest and most multifarious. They are converted by the automobile they're sitting in into a quasi-automaton and "the capacity for good or evil, for love or hatred" that interested Dickens in Hard Times is beside the point for the traffic planner. They become mere quantities that may be amenable to prediction and manipulation. But he accepts that in the more complicated scenes of human activity, this modelling seems to work only by simplifying the human being out of existence.

The notorious example is the perfectly rational, perfectly knowledgeable, perfectly avaricious human subject of old-fashioned political economy. Many of the studies Ball quotes are as crude and tedious as electronic ping-pong and one wonders if perhaps their devisers might profitably be doing something else. As Adam Smith wrote in his Astronomy, it is a constant temptation in philosophy to mistake scientific metaphors "for the real chains which Nature makes use of to bind together her several operations".

Occasionally, Ball does just that. After quoting a study that attempted to model why certain corporations backed the Unix computer operating code in the 1980s and why certain European countries joined the Axis powers on the eve of the second world war, Ball writes: "For a single model successfully to predict the allegiances of computer companies and the alliances during the descent into global war suggests that we have moved beyond the compartmentalised, case-dependent perspective of much traditional social and political science and hit a deeper seam in the order of things." Another way of looking at it is to say that to predict well-known public events several years after they have occurred is not perhaps the most demanding of tasks for an educated mind.

In a final chapter, fearful of having left a totalitarian impression, Ball retracts some of his claims for social physics and reminds us: "There are few things quite so misguided and dangerous as looking to science for moral guidance." Why then does he extend the authority of the hard sciences to these pedestrian and often footling essays in social science? It was precisely such claims to universal application that converted laisser faire and Marx's surplus value from mere commercial theories into implacable social moralities.

For this reviewer, far from social science gaining the precision of physics, physics has come to partake of the flakiness of economics. Rather than believing in the Efficient Markets Hypothesis, I have come to doubt the universal character of the Second Law of Thermo-dynamics. That was probably not Ball's intention, but it is a gift of incomparable sceptical value for which I will ever be in his debt.

· James Buchan's Capital of the Mind: How Edinburgh Changed the World is published by John Murray.